In recent years, two-channel complex-valued filterbanks have been studied and found theirs several important applications by many reseachers, such as complex signal and image processing. One of those important results is that there is no two-channel complex-valued linear-phase paraunitary filterbank (CLPPUFB), except for its filter lengths of 2. In this paper, we introduce a class of special complex-valued filterbanks which is a subclass of biorthogonal filterbanks: Those filterbanks are called complex pseudo-orthogonal filterbanks (CPOFB), based on the concept of pseudo-orthogonality (PO). This kind of orthogonality, we propose, is different from the conventional one essentially. This paper also shows possibility to design a two-channel complex linear-phase filterbank (CLPFB) with its filter lengths are more than 2, based on PO. Finally, we show a design example of a complex linear-phase pseudo-orthogonal filterbank (CLPPOFB). Moreover, such CPOFB can satisfy the linear-phase condition simultaneously with filter lengths are more than 2. This paper shows a theory, a design method and an example of CLPPOFB.